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Analysis of a Stochastic HBV Infection Model with DNA-Containing Capsids and Virions

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Abstract

In this paper, we propose a stochastic differential equation model which is used to explore how the environmental noise affects the spread of hepatitis B virus. Firstly, we show that there exists a unique global positive solution of the stochastic system with any positive initial value. Then, we adopt a stochastic Lyapunov function method to establish sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of the proposed stochastic model. Especially, under the same conditions as the existence of a stationary distribution, it is worth noting that we obtain the specific form of probability density around the quasi-infected steady state of the stochastic system. Thirdly, we obtain sufficient criteria for extinction of the infected hepatocytes. Finally, numerical simulations are introduced to validate the theoretical findings.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (No. 12001090) and the Jilin Provincial Science and Technology Development Plan Project (No. YDZJ202201ZYTS633).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Key Laboratory of Applied Statistics of MOE, Northeast Normal University, Changchun, 130024, Jilin Province, People’s Republic of China

    Qun Liu & Zhenfeng Shi

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  1. Qun Liu
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  2. Zhenfeng Shi
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Correspondence to Qun Liu.

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Communicated by Philip K. Main.

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Liu, Q., Shi, Z. Analysis of a Stochastic HBV Infection Model with DNA-Containing Capsids and Virions. J Nonlinear Sci 33, 23 (2023). https://doi.org/10.1007/s00332-022-09883-w

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  • DOI: https://doi.org/10.1007/s00332-022-09883-w

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